She was created using Liz's power that was siphoned by her, hence she was Lady Comstock physically (her dead body) but mentally she was what Liz thought she really was in her mind (the ghost's behaviour)

Rosalind Lutece speculates in a voxophone recording that the loss of her pinkie resulted in her powers saying, "What makes the girl different? I suspect it has less to do with what she is and more to do with what she's not. A small part of her remains from where she came. It would seem the universe does not like its peas with its porridge."

Rapture, and in that extent Bioshock 1 exist in Booker's timeline. Why? Remember that they never tell how Rapture was made to handle all the ocean pressure in the sea? What if there was someone in that timeline that is bright enough to discover how to handle that. And who else fit in this category than Robert Lutece? Robert came from the same timeline as Booker. And a person of his intelligence would have created something mind boggling. Why not an undersea city?